modelling and simulation of e ect of component sti ness on … · 2018-03-15 · length of the...

Modelling and simulation of effect ofcomponent stiffness on Dynamic

behaviour of Printed Circuit Board

M. Mary Thraza1, Somashekar V N2,Jayaraman S3, Manish Trikha4, Kamesh D5,

Venkatesh K6 and Ravindra M7

1Aurora Scientific & Technological College of Engineering,Hyderabad, India

2,3,4,5,6,7ISRO Satellite Centre,Vimanapura Post, Bangalore-560017,

Karnataka, [email protected]

January 5, 2018

Abstract

A spacecraft consists of a number of electronic packagesto meet the functional requirements. An electronic packageis generally an assembly of printed circuit boards placed in amechanical housing. A number of electronic components aremounted on the printed circuit board (PCB). A spacecraftexperiences various types of loads during its launch such asvibration, acoustic and shock loads. Prediction of responsefor printed circuit boards due to vibration loads is impor-tant for mechanical design and reliability of electronic pack-ages. The modeling and analysis of printed circuit boardsis required for accurate prediction of response due to vibra-tion loads. Vibration analyses of printed circuit boards arecarried out using finite element method. The objective ofthis paper is to predict the vibration response of a printed

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International Journal of Pure and Applied MathematicsVolume 118 No. 17 2018, 75-89ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu

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circuit board including the effect of component stiffness. Ef-fect of contribution of component stiffness to the dynamiccharacteristics of PCB assembly is investigated. Modelingand analyses of PCB with components used for space ap-plications is carried out. The analysis results are validatedusing vibration tests of PCB.

Key Words :Printed Circuit Board (PCB), Spacecraft,Vibration analysis, Component stiffness

1 Introduction

A spacecraft experiences various types of loads during its launchsuch as vibration, acoustic and shock loads. The electronic pack-ages are designed to withstand the launch vibration environment.Electronics packages are subjected to vibration testing to establishadequate margins. Package component failures due to vibrationloads have been observed in the past. The four basic failure modesof components mounted on PCB due to random vibration environ-ment are the results of the following conditions: high accelerationlevels, high stress levels, large displacement amplitudes and electri-cal signals out of tolerance [1].

It is possible to predict the probability of mechanical failure bya two stage Physics of Failure (POF) approach. The first stage ofthis approach is defined as the response prediction stage. In thisstage, vibration response of the board is calculated through a finiteelement (FE) model of the PCB component system. The secondstage relates this calculated response to some pre-determined com-ponent failure criteria, to show whether the attached componentscan withstand this curvature or acceleration.

Sophisticated electronic systems are often simulated using sim-ple masses, springs and dampers to estimate the dynamic character-istics of the system. Simple one and two degree of freedom systemsare used to approximate the electronic systems. More complicatedfinite element models of electronic systems are created to study thedynamic characteristics of the system and to estimate the fatiguelife of critical components mounted on the PCB. Finite elementmodels can be either simplified or detailed. Detailed finite ele-ment models are built by modeling the PCB and the components.

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However, this approach is rarely used as it is time consuming andexpensive. Instead, simplified models of PCB are created where thecomponents geometry is neglected. The component effects are in-cluded by increasing the Young’s modulus and density of the PCBFE model, so it effectively behaves as if components were present.The simple geometry of the board is modeled and meshed using2-D finite elements (i.e. by using flat shell elements). Sensitivityanalysis of PCB finite element models was carried out by Amy et al.[2]. They determined the factors of safety by using different sim-plification methods of modeling the PCB. Pitarresi [3], Pitarresi,et al. [4], and Pitarresi and Primavera [5] provided the solutionsfor issues encountered in modeling the PCB assembly that includeswide variety of components.

In this paper, modeling and simulation of a typical componentmounted on PCB used for space applications is carried out. First,vibration analysis of a bare PCB is carried out using FEM to de-termine the natural frequencies. The PCB is modeled using shellelements. The FEM model is validated by conducting vibrationtests on the PCB and comparing the simulation and test results.Next, static analysis of the component mounted on PCB is car-ried out to determine the contribution of component stiffness tothe PCB. The effect of the component stiffness to the PCB is cal-culated in terms of stiffness coefficients of the PCB based on thisanalysis. The stiffness coefficients give the effective stiffness of thePCB that includes the effect of component stiffness. The com-ponent is modeled using beam and shell elements. Subsequently,modal analysis and frequency response analysis are carried out fora PCB with components by using the stiffness coefficients derivedfrom the static analysis.

2 Vibration Analysis of a Bare PCB

In this study, a six layer PCB used for space applications is consid-ered. The PCB is modeled as isotropic plate with equivalent ma-terial properties such as Youngs modulus, Poissons ratio and massdensity. Details of the PCB are summarized in Table 1. The PCBis modelled using PATRAN as pre-processor and MSC.NASTRANis used as solver. The PCB is meshed with 1800 quadrilateral shell

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elements with appropriate thickness. Fixed /clamped boundaryconditions are applied at nine locations (PCB mounting locations)by arresting six degrees of freedom for the nodes on the boundaryof holes in PCB as shown in Figure [1].

Table 1: Details of PCB

Parameter ValuePCB size 2502002.1 mm

Mass of Bare PCB 208.4 gmYoungs Modulus of

Bare PCB20 GPa

Poissons ratio 0.12Boundary Condition Fixed/clamped

2.1 FE Simulation Model for Bare PCB

Normal mode analyses were conducted on FE model to extract firstthree fundamental natural frequencies for bare PCB. The calculatedfirst three natural frequencies are 318.7 Hz, 354.1 Hz and 368.1 Hzfor bare PCB. Mode shapes corresponding to these frequencies aregiven in Figures [2] to [4].

Figure 1: FE Model of bare PCBFigure 3: Mode shape of barePCB for second frequency

Figure 2: Mode shape of barePCB for first frequency

Figure 4: Mode shape of barePCB for third frequency

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2.2 2.2 Experimental Test Setup for Bare PCB

The vibration test was conducted by mounting the PCB with screwsat nine locations on vibration table. The bare PCB mounted on thevibration table is shown in Figure [5]. Accelerometers are mountedat various locations of the PCB to measure the responses. The vi-bration test was carried out in the vibration test facility consistingof electro-dynamic shaker, control system, signal conditioners anddata acquisition system. The frequency response function (FRF)is obtained using an electro-dynamic shaker by conducting a sinesweep test. In sine sweep test, the input acceleration is given to thetest specimen using electro-dynamic shaker and the output acceler-ation at various desired locations of the test specimen is measuredusing accelerometer. The ratio of output to input acceleration givesthe FRF at that location. The experimental frequency responseplot for bare PCB at a specific location is shown in Figure [6].

Figure 5: Bare PCB on VibrationTable

Figure 6: Experimental Fre-quency Response plot for barePCB

3 FEM Model Validation

The FEM model is validated by comparing the FEM simulation re-sults and the experimental test results. Simulation and test resultsfor fundamental frequencies of the bare PCB are compared in Table2. The simulation and test results for bare PCB are matching well.Hence the FEM model is validated.

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Table 2: Comparison of Fundamental Frequencies for Bare PCB

Mode No. Simulation Results (Hz) Test Results (Hz) % Difference

1 318.7 311 -2.47

2 354.1 351 -0.88

3 368.1 379 2.87

4 Static Analysis of a PCB with com-

ponent

Static analysis of the component mounted on PCB is carried outto determine the contribution of component stiffness to the PCB.The effect of the component stiffness to the PCB is calculated interms of stiffness coefficients of the PCB based on this analysis. Atypical component used in space applications is considered. Thecomponent consists of casing and the terminals (pins) as shown inFigure [7]. The component is mounted on the PCB by inserting theterminals in plated through holes and then soldering the terminalson PCB. The physical and material properties for the componentare given in Table 3 and Table 4. The component casing is modeledusing shell elements and terminals using beam elements.

The static analysis is carried out for a standard PCB size usedfor 3-point bending test. In 3-point bending test, the PCB is simplysupported at the ends and the load is transversely applied at themiddle of the PCB. First, the deformation is determined at the mid-point for a bare PCB and next for PCB with the component. Figure[8] shows the deformation plot of PCB with the component. Theratio of the deformations for first to second case gives the stiffnesscoefficient. The stiffness coefficient gives the effective stiffness of thePCB that includes the effect of component stiffness. This effectivestiffness of the PCB can used in local smearing approach at thecomponent footprint location.

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Table 3: Details of Componentand terminals

(L×B ×H)of component

20.57×10.41×2.1 mm

Length of the terminal 3 mm

Diameter of terminal 0.7 mm

Table 4: Properties of casing andterminals

Element Casing Terminal

Youngsmodulus

70 GPa 159 GPa

Density 8070 kg/m3 8000 kg/m3

Poissons ratio 0.33 0.33

Figure 7: Deformation of PCBwith component

Figure 8: Deformation plot ofPCB with component

Table 5: Linear Static Analysis of PCB With and Without Com-ponent

Analyticaldeformation

Bare PCB (withoutComponent)

PCB withComponent

Stiffness coefficient

2.54-004 m 2.65-004 m 1.31-004 m 2.02

5 Vibration Analysis of a PCB with com-

ponent

In this section, modal analysis and frequency response analysis arecarried out for a PCB with component. The component consideredfor static analysis is also taken for vibration analysis. The analysisis carried out for two cases. In the first case, the detailed modelingof the component with PCB is carried out. In the second case,the stiffness and mass of the component is simulated locally on thePCB.

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5.1 Detailed Modelling of PCB with Compo-nent

In this section, detailed modelling of the component is carried out.The component casing is modeled using shell elements and termi-nals using beam elements. The FE model of PCB with componentis shown in Figure [9]. Normal mode analyses were conducted onFE model to extract first three fundamental natural frequencies forPCB with component. The calculated first three natural frequen-cies are 324.0 Hz, 360.1 Hz and 385.0 Hz for PCB with component.Mode shapes corresponding to these frequencies are given in Figures[10] to [12].

Figure 9: FEM Model of PCBwith component

Figure 11: Mode shape of PCBwith component for second fre-quency

Figure 10: Mode shape of PCBwith component for first fre-quency

Figure 12: Mode shape of PCBwith component for third fre-quency

5.2 Modelling of PCB with Component usingLocal Smearing Approach

In this section, the stiffness and mass of the component is simulatedon the PCB using local smearing approach. An example of a locally

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smeared FE model of a PCB is shown in Figure 13. The effect ofcomponent on PCB is modelled by increasing the stiffness of PCBover the footprint of the component. The PCB density over thecomponent footprint includes the density of the component. Theequivalent Youngs Modulus of the PCB at the component footprintis given by Youngs Modulus of the bare PCB times the stiffnesscoefficient derived from the static analysis. Hence, Youngs Modulusof the PCB at the component footprint = 20*2.02=40.4 GPa.

Figure 13: Example of a locallysmeared FE model of a PCB

Figure15: Mode shape of locallysmeared PCB second frequency

Figure14: Mode shape of locallysmeared PCB first frequency

Figure16: Mode shape of locallysmeared PCB third frequency

6 Results and Discussions

In this section, the results of detailed modelling approach and thelocal smearing approach are compared. The natural frequencies ofthe PCB for two approaches are compared in Table 6. The re-sults are matching well. The maximum FRF for the second naturalfrequency at the component location is shown in Figure 17 andFigure 18 and compared in Table 7. These results also show good

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agreement. Hence local smearing approach is also appropriate fordetermination of natural frequencies and the FRF. This is especiallyuseful for modelling of PCB mounted with number of components.Detailed component modelling, which is time consuming can beavoided. Instead, local smearing approach can be applied basedon the stiffness coefficients obtained for the components. The stiff-ness coefficients can be obtained by simulation or experimentallyfor different type of components.

Table 6: Comparison of Natural Frequencies of PCB with compo-nent for different approaches

Mode No.Natural Frequency

(Hz)Detailed modelling Local smearing

1 328 3242 363 3603 385 385

Figure17: FRF Plot at Component Location for detailed modellingapproach

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Figure18: FRF Plot at Component Location for local smearingapproach

Table 7: Comparison of FRF at component location for differentapproaches

Approach FRFDetailed modelling 6.0

Local smearing 5.9

7 Detailed Modelling for Component Stresses

/ Strains

For determination of stresses/strains for the component or at thePCB-component interface, detailed modelling approach is required.Stresses/strains for a base excitation of 100 m/s2 is determined us-ing detailed modelling of the component on the PCB. The strainplots for the PCB and maximum strains at PCB-terminal inter-face are shown in Figures 17-18. The maximum strains at PCB-terminal interface occur for the outer terminals of the component.The maximum strains at PCB-terminal interface for first three nat-ural frequencies are shown in Table 7. The strains are maximumfor the third natural frequency. The stress plots for the PCB andmaximum stresses at PCB-terminal interface are shown in Figures19-20. The maximum stresses (axial and bending) for componentterminal for first 3 natural frequencies are shown in Table 8. Theterminal maximum bending stress occurs for the outer terminal for

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the third natural frequency.

Figure 19: Stain plot for PCBFigure 20: Maximum strain atPCB-terminal interface

Table 8: Comparison of maximum strains at PCB-terminal inter-face for natural frequencies

ModeNo

Natural Frequency(Hz)

Maximum strains at PCB -terminal interface ()

1 326 18.62 361 32.63 386 47.4

Figure 21: Stress plot for PCBFigure 22: Maximum stress atPCB-terminal interface

Table 9: Comparison of maximum stresses for component terminalfor natural frequencies

ModeNo

Natural Frequency(Hz)

Terminal MaximumAxial Stress (MPa)

Terminal MaximumBending stress (MPa)

1 326 1.95 4.442 361 2.57 7.773 386 1.93 11.3

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8 Conclusions

Vibration analysis of a printed circuit board is carried out includingthe effect of component stiffness. For model validation, the FEMsimulation results are compared with experimental test results forbare PCB. The vibration analysis of a typical PCB mounted witha component is carried out using two different approaches: detailedcomponent modelling approach and local smearing approach. Forlocal smearing approach, the effect of the component stiffness tothe PCB is calculated in terms of stiffness coefficients of the PCBbased on static analysis. The results of detailed modelling approachand the local smearing approach are matching well for the naturalfrequencies and FRF. Hence local smearing approach is appropri-ate for determination of natural frequencies and the FRF, sincedetailed component modelling approach is time consuming. De-tailed component modelling approach is required for determinationof stresses/strains for the component or at the PCB-componentinterface. The maximum stresses and strains at PCB-terminal in-terface occur for the outer terminals of the component.

Acknowledgement

The authors would like to thank Shri K. Venkatesh, Group Di-rector, QAG, Md. Khan Assistant Professor, and Dr. M. Ravin-dra, Deputy Director, RCA for their constant support during thisproject. This team is also thankful to Mr. E. Dinakaran, Head, andOnboard Computers section, also thankful to Mr. Nawab SystemEngineer.

References

[1] Steinberg D. S., Vibration Analysis for Electronic Equipment.3rd ed. New York: John Wiley & Sons Inc., 2000.

[2] Amy R. A., Aglietti G. S., Richardson G.,Sensitivity analy-sis of simplified Printed Circuit Board finite element models,Microelectronics Reliability, Vol. 49, pp. 791-799, 2009.

[3] Pitarresi, J.M., Modeling of Printed Circuit Cards Subject toVibration, IEEE Proceedings of the Circuits and Systems Con-ference, New Orleans, LA, May 3-5, pp. 2104-2107, 1990.

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[4] Pitarresi J.M., Celetka D., Coldwel R. and Smith D., TheSmeared Properties Approach to FE Vibration Modeling ofPrinted Circuit Cards, ASME Journal of Electronics Packag-ing, Vol.113, pp. 250-257, 1991.

[5] Pitarresi J.M. and Primavera A., Comparison of VibrationModeling Techniques for Printed Circuit Cards, ASME Journalof Electronics Packaging, Vol.113, pp. 378-383, 1992

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